Quelle floor_div_lems.prf Sprache: Lisp

(floor_div_lems
(floor_small_nat 0
  (floor_small_nat-1 nil 3507028513
   ("" (skosimp*)
    (("" (assert)
      (("" (lemma "floor_small")
        (("" (inst?) (("" (expand "abs") (("" (propax) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (integer nonempty-type-from-decl nil integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (nonzero_integer nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (floor_small formula-decl nil floor_ceil nil))
   nil))
(is_multiple 0
  (is_multiple-1 nil 3507028513
   ("" (skosimp*)
    (("" (iff 1)
      (("" (split 1)
        (("1" (flatten)
          (("1" (inst 1 "i!1/j!1") (("1" (assert) nil)))))
         ("2" (flatten) (("2" (skosimp*) (("2" (assert) nil))))))))))
    nil)
   ((mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (rat_times_rat_is_rat application-judgement "rat" rationals nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (int nonempty-type-eq-decl nil integers nil)
    (i!1 skolem-const-decl "int" floor_div_lems nil)
    (nonzero_integer nonempty-type-eq-decl nil integers nil)
    (j!1 skolem-const-decl "nonzero_integer" floor_div_lems nil)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil))
   nil)))

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